This lecture covers the concept of Markov chains and their applications in algorithms, focusing on topics such as exact simulation by coupling from the past and random mapping. The instructor explains the theory behind Markov chains and demonstrates how they can be used in algorithm design. The lecture also delves into Propp-Wilson algorithms and theorems related to Markov chains. Various theorems are presented, including those by Propp and Wilson in 1986, discussing the behavior of chains with initial states and their convergence over time.